D1 June 2014 (R) Q1
1.
31 10 38 45 19 47 35 28 12
| Scheme | Marks |
|---|---|
| Bin 1: \(\boxed{31}\ \ \boxed{10}\ \ \underline{19}\) | M1 A1 A1 |
| Bin 2: \(\boxed{38}\ \ 12\) | |
| Bin 3: \(\boxed{45}\) | |
| Bin 4: \(\underline{47}\) | |
| Bin 5: \(\underline{35}\) | |
| Bin 6: \(\underline{28}\) | |
| (3) |
Notes
a1M1: First four items placed correctly in bins 1, 2 and 3. (Condone cumulative totals here only.)
a1A1: First eight terms placed correctly.
a2A1: CSO – all correct.
| Scheme | Marks |
|---|---|
| e.g. middle right | |
| \(31\quad 10\quad 38\quad 45\quad \boxed{19}\quad 47\quad 35\quad 28\quad 12\) Pivot 19 | M1 |
| \(31\quad 38\quad 45\quad \boxed{47}\quad 35\quad 28\quad \boxed{19}\quad 10\quad \boxed{12}\) Pivots 47, 12 | A1 |
| \(\boxed{47}\quad 31\quad 38\quad \boxed{45}\quad 35\quad 28\quad \boxed{19}\quad \boxed{12}\quad \boxed{10}\) Pivots 45 (10) | |
| \(\boxed{47}\quad \boxed{45}\quad 31\quad 38\quad \boxed{35}\quad 28\quad \boxed{19}\quad \boxed{12}\quad \boxed{10}\) Pivot 35 | A1ft |
| \(\boxed{47}\quad \boxed{45}\quad \boxed{38}\quad \boxed{35}\quad 31\quad \boxed{28}\quad \boxed{19}\quad \boxed{12}\quad \boxed{10}\) Pivot 28 (38) | |
| \(\boxed{47}\quad \boxed{45}\quad \boxed{38}\quad \boxed{35}\quad \boxed{31}\quad \boxed{28}\quad \boxed{19}\quad \boxed{12}\quad \boxed{10}\) (sort complete) | A1 |
| (4) |
Notes
b1M1: Quick sort – pivots, p, selected and first pass gives <p, p, >p. If only choosing one pivot per iteration M1 only.
b1A1: First pass correct, next two pivots chosen correctly for second pass.
b2A1ft: Second and third passes correct (follow through from their first pass and choice of pivots) – and net pivot(s) chosen consistently for fourth pass.
b3A1: CSO including choice of pivots for the fifth pass and ‘sort complete’ – this could be shown either by a ‘stop’ statement or final list being re-written or using each item as a pivot.
Sorting list into ascending order in (b)
- If the candidate sorts the list into ascending order and reverse the list in (b) then they can score full marks in (b).
- If the list is not reversed in (b) then mark as a misread (so remove the last two A marks earned in (b)). If the list is reversed at the start of (c) but not in (b) then still treat this as a misread. If the list is still in ascending order in (c) award no marks for first fit increasing. If the candidate says that the list needs reversing in (b) but doesn’t actually show the reversed list in (b) then remove the final A mark in (b).
Misreads
- If they have misread a number at the start of (a), so genuinely miscopied a number (before starting the question) then please mark the whole question as a misread (so remove the final two A/B marks earned).
- If they make an error during the quick sort then mark this as an error. They can still earn the M mark in (c) (see SC in (c)).
Middle left
| \(31\quad 10\quad 38\quad 45\quad \boxed{19}\quad 47\quad 35\quad 28\quad 12\) Pivot 19 | |
| \(31\quad 38\quad \boxed{45}\quad 47\quad 35\quad 28\quad \boxed{19}\quad \boxed{10}\quad 12\) Pivot 45, 10 | M1 A1 |
| \(\boxed{47}\quad \boxed{45}\quad 31\quad \boxed{38}\quad 35\quad 28\quad \boxed{19}\quad \boxed{12}\quad \boxed{10}\) Pivot (47), 38, (12) | |
| \(\boxed{47}\quad \boxed{45}\quad \boxed{38}\quad 31\quad \boxed{35}\quad 28\quad \boxed{19}\quad \boxed{12}\quad \boxed{10}\) Pivot 35 | A1ft |
| \(\boxed{47}\quad \boxed{45}\quad \boxed{38}\quad \boxed{35}\quad \boxed{31}\quad 28\quad \boxed{19}\quad \boxed{12}\quad \boxed{10}\) Pivot 31 | |
| \(\boxed{47}\quad \boxed{45}\quad \boxed{38}\quad \boxed{35}\quad \boxed{31}\quad \boxed{28}\quad \boxed{19}\quad \boxed{12}\quad \boxed{10}\) list in order | A1cso |
Ascending order (middle right)
| \(31\quad 10\quad 38\quad 45\quad \boxed{19}\quad 47\quad 35\quad 28\quad 12\) Pivot 19 | |
| \(10\quad \boxed{12}\quad \boxed{19}\quad 31\quad 38\quad 45\quad \boxed{47}\quad 35\quad 28\) Pivot 12, 47 | M1 A1 |
| \(\boxed{10}\quad \boxed{12}\quad \boxed{19}\quad 31\quad 38\quad \boxed{45}\quad 35\quad 28\quad \boxed{47}\) Pivot (10), 45 | |
| \(\boxed{10}\quad \boxed{12}\quad \boxed{19}\quad 31\quad 38\quad \boxed{35}\quad 28\quad \boxed{45}\quad \boxed{47}\) Pivot 35 | A1ft |
| \(\boxed{10}\quad \boxed{12}\quad \boxed{19}\quad 31\quad \boxed{28}\quad \boxed{35}\quad \boxed{38}\quad \boxed{45}\quad \boxed{47}\) Pivot 28, (38) | |
| \(\boxed{10}\quad \boxed{12}\quad \boxed{19}\quad \boxed{28}\quad \boxed{31}\quad \boxed{35}\quad \boxed{38}\quad \boxed{45}\quad \boxed{47}\) list in order | A1cso |
Ascending order (middle left)
| \(31\quad 10\quad 38\quad 45\quad \boxed{19}\quad 47\quad 35\quad 28\quad 12\) Pivot 19 | |
| \(\boxed{10}\quad 12\quad \boxed{19}\quad 31\quad 38\quad \boxed{45}\quad 47\quad 35\quad 28\) Pivot 10, 45 | M1 A1 |
| \(\boxed{10}\quad \boxed{12}\quad \boxed{19}\quad 31\quad \boxed{38}\quad 35\quad 28\quad \boxed{45}\quad \boxed{47}\) Pivot (12), 38, (47) | |
| \(\boxed{10}\quad \boxed{12}\quad \boxed{19}\quad 31\quad \boxed{35}\quad 28\quad \boxed{38}\quad \boxed{45}\quad \boxed{47}\) Pivot 35 | A1ft |
| \(\boxed{10}\quad \boxed{12}\quad \boxed{19}\quad \boxed{31}\quad 28\quad \boxed{35}\quad \boxed{38}\quad \boxed{45}\quad \boxed{47}\) Pivot 31 | |
| \(\boxed{10}\quad \boxed{12}\quad \boxed{19}\quad \boxed{28}\quad \boxed{31}\quad \boxed{35}\quad \boxed{38}\quad \boxed{45}\quad \boxed{47}\) list in order | A1cso |
| Scheme | Marks |
|---|---|
| Bin 1: \(\boxed{47}\ \ 12\) | M1 A1 |
| Bin 2: \(\boxed{45}\ \ 10\) | |
| Bin 3: \(\boxed{38}\ \ \boxed{19}\) | |
| Bin 4: \(\boxed{35}\) | |
| Bin 5: \(\boxed{31}\ \ \boxed{28}\) | |
| (2) |
Notes
c1M1: Must be using list in descending order (independent of (b)). First seven terms placed correctly.
c1A1: CAO
SC for (c): if the ‘sorted’ list they use in (c) has one ‘error’ from (b) (e.g. a missing number, an extra number or one number incorrectly placed) then M1 only can be awarded in (c) (for the first seven items). If there is more than one ‘error’ then M0. Allow full marks in (c) if a correct list is used in (c) even if the list is incorrect at the end of (b).
| Scheme | Marks |
|---|---|
| \(\dfrac{265}{60} \approx 4.417\) so yes 5 bins is optimal | M1 A1 |
| (2) | |
| (11 marks) |
Notes
d1M1: E.g. Attempt to find lower bound \((265 \pm 47)/60\), (oe) could remark on number of items \(>30\). The argument must be numerical in nature.
d1A1: CSO including 5.